A spring-powered dart gun is unstretched and has a spring constant 16.0 N/m. The spring is compressed by 8.0 cm and a 5.0 gram projectile is placed in the gun. The kinetic energy of the projectile when it is shot from the gun is

Given that,

Spring constant = 16N/m

Extension of spring

x = 8cm = 0.08m

Mass

m = 5g = 5/1000 = 0.005 kg

The ball will leave with a speed that makes its kinetic energy equal to the potential energy of the compressed spring.

So, Using conservation of energy

Energy in spring is converted to kinectic energy

So, Ux = K. E

Ux = ½ kx²

Then,

Ux = ½ * 16 * 0.08m²

Ux = 0.64 J

Since, K. E = Ux

K. E = 0.64 J